# Copyright (C) PROWLER.io 2017
#
# Licensed under the Apache License, Version 2.0

# pylint: skip-file
# (Pylint takes a long time to process this file due to its length and it's just a look-up table,
# so let's skip it.)

import numpy as np

# lookup table provided by Chris Lloyd

__G_lookup_table = list(map(np.array, [
    # G1 is G evaluated at z = -1:0.001:0;
    [0, -0.0019993335, -0.0039973348, -0.0059940048, -0.0079893447,
     -0.0099833555, -0.011976038, -0.013967394, -0.015957424,
     -0.017946129, -0.019933511, -0.021919569, -0.023904306, -0.025887723,
     -0.027869820, -0.029850598, -0.031830059, -0.033808204, -0.035785033,
     -0.037760548, -0.039734749, -0.041707639, -0.043679217, -0.045649486,
     -0.047618445, -0.049586096, -0.051552441, -0.053517479, -0.055481213,
     -0.057443642, -0.059404769, -0.061364595, -0.063323119, -0.065280344,
     -0.067236270, -0.069190899, -0.071144231, -0.073096267, -0.075047009,
     -0.076996458, -0.078944614, -0.080891479, -0.082837054, -0.084781339,
     -0.086724335, -0.088666045, -0.090606468, -0.092545606, -0.094483460,
     -0.096420031, -0.098355320, -0.10028933, -0.10222205, -0.10415350,
     -0.10608367, -0.10801257, -0.10994018, -0.11186653, -0.11379159,
     -0.11571539, -0.11763791, -0.11955916, -0.12147915, -0.12339786,
     -0.12531530, -0.12723148, -0.12914640, -0.13106004, -0.13297243,
     -0.13488355, -0.13679341, -0.13870201, -0.14060934, -0.14251542,
     -0.14442025, -0.14632381, -0.14822612, -0.15012717, -0.15202697,
     -0.15392552, -0.15582282, -0.15771886, -0.15961366, -0.16150720,
     -0.16339950, -0.16529055, -0.16718036, -0.16906892, -0.17095623,
     -0.17284231, -0.17472714, -0.17661073, -0.17849308, -0.18037419,
     -0.18225407, -0.18413270, -0.18601011, -0.18788627, -0.18976120,
     -0.19163490, -0.19350737, -0.19537860, -0.19724861, -0.19911739,
     -0.20098493, -0.20285125, -0.20471635, -0.20658022, -0.20844286,
     -0.21030429, -0.21216449, -0.21402346, -0.21588122, -0.21773776,
     -0.21959308, -0.22144718, -0.22330007, -0.22515174, -0.22700219,
     -0.22885144, -0.23069947, -0.23254628, -0.23439189, -0.23623629,
     -0.23807948, -0.23992146, -0.24176223, -0.24360180, -0.24544016,
     -0.24727732, -0.24911328, -0.25094803, -0.25278158, -0.25461394,
     -0.25644509, -0.25827504, -0.26010380, -0.26193136, -0.26375773,
     -0.26558290, -0.26740688, -0.26922966, -0.27105126, -0.27287166,
     -0.27469087, -0.27650890, -0.27832573, -0.28014138, -0.28195584,
     -0.28376912, -0.28558122, -0.28739213, -0.28920186, -0.29101040,
     -0.29281777, -0.29462396, -0.29642897, -0.29823280, -0.30003545,
     -0.30183693, -0.30363724, -0.30543637, -0.30723433, -0.30903111,
     -0.31082673, -0.31262117, -0.31441445, -0.31620655, -0.31799749,
     -0.31978727, -0.32157588, -0.32336332, -0.32514960, -0.32693472,
     -0.32871867, -0.33050146, -0.33228310, -0.33406357, -0.33584289,
     -0.33762105, -0.33939805, -0.34117390, -0.34294860, -0.34472214,
     -0.34649452, -0.34826576, -0.35003585, -0.35180478, -0.35357257,
     -0.35533920, -0.35710469, -0.35886904, -0.36063224, -0.36239429,
     -0.36415520, -0.36591497, -0.36767360, -0.36943109, -0.37118743,
     -0.37294264, -0.37469671, -0.37644964, -0.37820143, -0.37995209,
     -0.38170162, -0.38345001, -0.38519727, -0.38694339, -0.38868839,
     -0.39043226, -0.39217499, -0.39391660, -0.39565708, -0.39739644,
     -0.39913466, -0.40087177, -0.40260775, -0.40434261, -0.40607634,
     -0.40780895, -0.40954045, -0.41127082, -0.41300008, -0.41472822,
     -0.41645524, -0.41818114, -0.41990593, -0.42162961, -0.42335217,
     -0.42507362, -0.42679396, -0.42851319, -0.43023131, -0.43194832,
     -0.43366422, -0.43537901, -0.43709270, -0.43880529, -0.44051676,
     -0.44222714, -0.44393641, -0.44564458, -0.44735165, -0.44905762,
     -0.45076249, -0.45246626, -0.45416894, -0.45587051, -0.45757099,
     -0.45927038, -0.46096867, -0.46266587, -0.46436198, -0.46605699,
     -0.46775092, -0.46944375, -0.47113550, -0.47282616, -0.47451573,
     -0.47620421, -0.47789161, -0.47957792, -0.48126315, -0.48294730,
     -0.48463037, -0.48631235, -0.48799325, -0.48967308, -0.49135182,
     -0.49302949, -0.49470608, -0.49638159, -0.49805603, -0.49972940,
     -0.50140169, -0.50307291, -0.50474305, -0.50641213, -0.50808013,
     -0.50974707, -0.51141294, -0.51307773, -0.51474147, -0.51640413,
     -0.51806573, -0.51972627, -0.52138574, -0.52304415, -0.52470150,
     -0.52635779, -0.52801302, -0.52966719, -0.53132030, -0.53297235,
     -0.53462334, -0.53627328, -0.53792217, -0.53957000, -0.54121677,
     -0.54286249, -0.54450717, -0.54615079, -0.54779336, -0.54943488,
     -0.55107535, -0.55271477, -0.55435315, -0.55599048, -0.55762677,
     -0.55926201, -0.56089621, -0.56252936, -0.56416148, -0.56579255,
     -0.56742258, -0.56905157, -0.57067952, -0.57230644, -0.57393232,
     -0.57555716, -0.57718097, -0.57880374, -0.58042548, -0.58204618,
     -0.58366585, -0.58528449, -0.58690210, -0.58851868, -0.59013424,
     -0.59174876, -0.59336226, -0.59497472, -0.59658617, -0.59819659,
     -0.59980598, -0.60141435, -0.60302170, -0.60462803, -0.60623333,
     -0.60783762, -0.60944088, -0.61104313, -0.61264436, -0.61424458,
     -0.61584377, -0.61744195, -0.61903912, -0.62063527, -0.62223041,
     -0.62382454, -0.62541766, -0.62700976, -0.62860086, -0.63019094,
     -0.63178002, -0.63336809, -0.63495516, -0.63654122, -0.63812627,
     -0.63971032, -0.64129336, -0.64287541, -0.64445645, -0.64603649,
     -0.64761553, -0.64919357, -0.65077061, -0.65234665, -0.65392170,
     -0.65549575, -0.65706880, -0.65864086, -0.66021192, -0.66178199,
     -0.66335107, -0.66491916, -0.66648625, -0.66805236, -0.66961747,
     -0.67118160, -0.67274474, -0.67430689, -0.67586806, -0.67742824,
     -0.67898743, -0.68054564, -0.68210287, -0.68365911, -0.68521438,
     -0.68676866, -0.68832196, -0.68987428, -0.69142563, -0.69297599,
     -0.69452538, -0.69607379, -0.69762123, -0.69916769, -0.70071318,
     -0.70225769, -0.70380123, -0.70534380, -0.70688540, -0.70842603,
     -0.70996569, -0.71150438, -0.71304210, -0.71457885, -0.71611464,
     -0.71764946, -0.71918332, -0.72071621, -0.72224814, -0.72377910,
     -0.72530911, -0.72683815, -0.72836623, -0.72989335, -0.73141952,
     -0.73294472, -0.73446897, -0.73599226, -0.73751459, -0.73903597,
     -0.74055639, -0.74207587, -0.74359438, -0.74511195, -0.74662856,
     -0.74814422, -0.74965894, -0.75117270, -0.75268551, -0.75419738,
     -0.75570830, -0.75721827, -0.75872730, -0.76023538, -0.76174252,
     -0.76324871, -0.76475396, -0.76625827, -0.76776164, -0.76926407,
     -0.77076556, -0.77226611, -0.77376572, -0.77526439, -0.77676212,
     -0.77825892, -0.77975479, -0.78124972, -0.78274371, -0.78423678,
     -0.78572890, -0.78722010, -0.78871037, -0.79019971, -0.79168811,
     -0.79317559, -0.79466214, -0.79614776, -0.79763246, -0.79911623,
     -0.80059907, -0.80208099, -0.80356198, -0.80504206, -0.80652121,
     -0.80799943, -0.80947674, -0.81095313, -0.81242860, -0.81390314,
     -0.81537677, -0.81684949, -0.81832128, -0.81979216, -0.82126213,
     -0.82273118, -0.82419931, -0.82566654, -0.82713285, -0.82859825,
     -0.83006273, -0.83152631, -0.83298898, -0.83445074, -0.83591159,
     -0.83737153, -0.83883057, -0.84028870, -0.84174592, -0.84320224,
     -0.84465766, -0.84611217, -0.84756578, -0.84901849, -0.85047030,
     -0.85192120, -0.85337121, -0.85482032, -0.85626853, -0.85771584,
     -0.85916225, -0.86060777, -0.86205239, -0.86349612, -0.86493895,
     -0.86638089, -0.86782194, -0.86926209, -0.87070136, -0.87213973,
     -0.87357721, -0.87501380, -0.87644951, -0.87788432, -0.87931825,
     -0.88075129, -0.88218345, -0.88361472, -0.88504511, -0.88647461,
     -0.88790323, -0.88933096, -0.89075782, -0.89218379, -0.89360889,
     -0.89503310, -0.89645643, -0.89787889, -0.89930047, -0.90072117,
     -0.90214099, -0.90355994, -0.90497801, -0.90639521, -0.90781154,
     -0.90922699, -0.91064157, -0.91205528, -0.91346812, -0.91488008,
     -0.91629118, -0.91770141, -0.91911077, -0.92051926, -0.92192689,
     -0.92333365, -0.92473954, -0.92614457, -0.92754873, -0.92895203,
     -0.93035447, -0.93175604, -0.93315676, -0.93455661, -0.93595560,
     -0.93735374, -0.93875101, -0.94014742, -0.94154298, -0.94293768,
     -0.94433153, -0.94572452, -0.94711665, -0.94850793, -0.94989835,
     -0.95128793, -0.95267665, -0.95406452, -0.95545153, -0.95683770,
     -0.95822302, -0.95960749, -0.96099111, -0.96237388, -0.96375580,
     -0.96513688, -0.96651712, -0.96789650, -0.96927505, -0.97065275,
     -0.97202960, -0.97340561, -0.97478079, -0.97615512, -0.97752861,
     -0.97890126, -0.98027307, -0.98164404, -0.98301417, -0.98438347,
     -0.98575193, -0.98711955, -0.98848634, -0.98985229, -0.99121741,
     -0.99258170, -0.99394515, -0.99530777, -0.99666956, -0.99803052,
     -0.99939064, -1.0007499, -1.0021084, -1.0034661, -1.0048229,
     -1.0061788, -1.0075340, -1.0088883, -1.0102418, -1.0115945,
     -1.0129464, -1.0142974, -1.0156476, -1.0169970, -1.0183456,
     -1.0196934, -1.0210403, -1.0223864, -1.0237317, -1.0250762,
     -1.0264198, -1.0277626, -1.0291047, -1.0304459, -1.0317863,
     -1.0331258, -1.0344646, -1.0358026, -1.0371397, -1.0384760,
     -1.0398115, -1.0411462, -1.0424801, -1.0438132, -1.0451455,
     -1.0464769, -1.0478076, -1.0491375, -1.0504665, -1.0517947,
     -1.0531222, -1.0544488, -1.0557746, -1.0570996, -1.0584239,
     -1.0597473, -1.0610699, -1.0623917, -1.0637127, -1.0650329,
     -1.0663524, -1.0676710, -1.0689888, -1.0703058, -1.0716220,
     -1.0729375, -1.0742521, -1.0755659, -1.0768790, -1.0781912,
     -1.0795027, -1.0808134, -1.0821232, -1.0834323, -1.0847406,
     -1.0860481, -1.0873548, -1.0886608, -1.0899659, -1.0912703,
     -1.0925738, -1.0938766, -1.0951786, -1.0964798, -1.0977802,
     -1.0990799, -1.1003787, -1.1016768, -1.1029741, -1.1042706,
     -1.1055663, -1.1068613, -1.1081554, -1.1094488, -1.1107414,
     -1.1120333, -1.1133243, -1.1146146, -1.1159041, -1.1171928,
     -1.1184808, -1.1197680, -1.1210544, -1.1223400, -1.1236249,
     -1.1249090, -1.1261923, -1.1274748, -1.1287566, -1.1300376,
     -1.1313178, -1.1325973, -1.1338760, -1.1351539, -1.1364311,
     -1.1377075, -1.1389831, -1.1402580, -1.1415321, -1.1428055,
     -1.1440780, -1.1453499, -1.1466209, -1.1478912, -1.1491607,
     -1.1504295, -1.1516975, -1.1529648, -1.1542313, -1.1554970,
     -1.1567620, -1.1580262, -1.1592897, -1.1605524, -1.1618143,
     -1.1630755, -1.1643360, -1.1655957, -1.1668546, -1.1681128,
     -1.1693703, -1.1706270, -1.1718829, -1.1731381, -1.1743925,
     -1.1756462, -1.1768991, -1.1781513, -1.1794028, -1.1806535,
     -1.1819034, -1.1831527, -1.1844011, -1.1856488, -1.1868958,
     -1.1881420, -1.1893875, -1.1906323, -1.1918763, -1.1931196,
     -1.1943621, -1.1956039, -1.1968449, -1.1980852, -1.1993248,
     -1.2005636, -1.2018017, -1.2030391, -1.2042757, -1.2055116,
     -1.2067468, -1.2079812, -1.2092149, -1.2104479, -1.2116801,
     -1.2129116, -1.2141423, -1.2153724, -1.2166017, -1.2178302,
     -1.2190581, -1.2202852, -1.2215116, -1.2227372, -1.2239622,
     -1.2251864, -1.2264098, -1.2276326, -1.2288546, -1.2300759,
     -1.2312965, -1.2325164, -1.2337355, -1.2349539, -1.2361716,
     -1.2373886, -1.2386049, -1.2398204, -1.2410352, -1.2422493,
     -1.2434627, -1.2446753, -1.2458873, -1.2470985, -1.2483090,
     -1.2495188, -1.2507279, -1.2519363, -1.2531439, -1.2543509,
     -1.2555571, -1.2567626, -1.2579674, -1.2591715, -1.2603749,
     -1.2615776, -1.2627795, -1.2639808, -1.2651813, -1.2663812,
     -1.2675803, -1.2687787, -1.2699764, -1.2711735, -1.2723698,
     -1.2735654, -1.2747603, -1.2759545, -1.2771480, -1.2783407,
     -1.2795328, -1.2807242, -1.2819149, -1.2831049, -1.2842942,
     -1.2854828, -1.2866707, -1.2878579, -1.2890444, -1.2902302,
     -1.2914153, -1.2925997, -1.2937834, -1.2949664, -1.2961487,
     -1.2973303, -1.2985113, -1.2996915, -1.3008711, -1.3020499,
     -1.3032281, -1.3044055, -1.3055823, -1.3067584, -1.3079338,
     -1.3091085, -1.3102826, -1.3114559, -1.3126286, -1.3138005,
     -1.3149718, -1.3161424, -1.3173123, -1.3184815, -1.3196501,
     -1.3208179, -1.3219851, -1.3231516, -1.3243174, -1.3254826,
     -1.3266470, -1.3278108, -1.3289739, -1.3301363, -1.3312980,
     -1.3324590, -1.3336194, -1.3347791, -1.3359381, -1.3370965,
     -1.3382541, -1.3394111, -1.3405675, -1.3417231, -1.3428781,
     -1.3440324, -1.3451860, -1.3463389, -1.3474912, -1.3486428,
     -1.3497938, -1.3509440, -1.3520936, -1.3532426, -1.3543908,
     -1.3555384, -1.3566853, -1.3578316, -1.3589772, -1.3601221,
     -1.3612664, -1.3624100, -1.3635529, -1.3646952, -1.3658368,
     -1.3669777, -1.3681180, -1.3692576, -1.3703965, -1.3715348,
     -1.3726725, -1.3738094, -1.3749458, -1.3760814, -1.3772164,
     -1.3783507, -1.3794844, -1.3806174, -1.3817498, -1.3828815,
     -1.3840125, -1.3851429, -1.3862727, -1.3874018, -1.3885302,
     -1.3896580, -1.3907851, -1.3919116, -1.3930374, -1.3941626,
     -1.3952871, -1.3964110, -1.3975342, -1.3986568, -1.3997787,
     -1.4009000, -1.4020206, -1.4031406, -1.4042599, -1.4053786,
     -1.4064966, -1.4076140, -1.4087308, -1.4098469, -1.4109623,
     -1.4120772, -1.4131913, -1.4143049, -1.4154178, -1.4165300,
     -1.4176416, -1.4187526, -1.4198629, -1.4209726, -1.4220817,
     -1.4231901, -1.4242978, -1.4254050, -1.4265115, -1.4276173,
     -1.4287226, -1.4298271, -1.4309311, -1.4320344, -1.4331371,
     -1.4342392, -1.4353406, -1.4364414, -1.4375415, -1.4386410,
     -1.4397399, -1.4408382, -1.4419358, -1.4430328, -1.4441292,
     -1.4452249, -1.4463200, -1.4474145, -1.4485083, -1.4496016,
     -1.4506942, -1.4517861, -1.4528775, -1.4539682, -1.4550583,
     -1.4561478, -1.4572366, -1.4583248, -1.4594124, -1.4604994,
     -1.4615858, -1.4626715, -1.4637566, -1.4648411, -1.4659250,
     -1.4670082, -1.4680909, -1.4691729, -1.4702543, -1.4713351,
     -1.4724152, -1.4734948, -1.4745737, -1.4756520, -1.4767297,
     -1.4778068, -1.4788833],

    # G2 is G evaluated at z = -10:0.01:0;
    [0, -0.019933511, -0.039734749, -0.059404769, -0.078944614,
     -0.098355320, -0.11763791, -0.13679341, -0.15582282, -0.17472714,
     -0.19350737, -0.21216449, -0.23069947, -0.24911328, -0.26740688,
     -0.28558122, -0.30363724, -0.32157588, -0.33939805, -0.35710469,
     -0.37469671, -0.39217499, -0.40954045, -0.42679396, -0.44393641,
     -0.46096867, -0.47789161, -0.49470608, -0.51141294, -0.52801302,
     -0.54450717, -0.56089621, -0.57718097, -0.59336226, -0.60944088,
     -0.62541766, -0.64129336, -0.65706880, -0.67274474, -0.68832196,
     -0.70380123, -0.71918332, -0.73446897, -0.74965894, -0.76475396,
     -0.77975479, -0.79466214, -0.80947674, -0.82419931, -0.83883057,
     -0.85337121, -0.86782194, -0.88218345, -0.89645643, -0.91064157,
     -0.92473954, -0.93875101, -0.95267665, -0.96651712, -0.98027307,
     -0.99394515, -1.0075340, -1.0210403, -1.0344646, -1.0478076,
     -1.0610699, -1.0742521, -1.0873548, -1.1003787, -1.1133243,
     -1.1261923, -1.1389831, -1.1516975, -1.1643360, -1.1768991,
     -1.1893875, -1.2018017, -1.2141423, -1.2264098, -1.2386049,
     -1.2507279, -1.2627795, -1.2747603, -1.2866707, -1.2985113,
     -1.3102826, -1.3219851, -1.3336194, -1.3451860, -1.3566853,
     -1.3681180, -1.3794844, -1.3907851, -1.4020206, -1.4131913,
     -1.4242978, -1.4353406, -1.4463200, -1.4572366, -1.4680909,
     -1.4788833, -1.4896142, -1.5002842, -1.5108937, -1.5214431,
     -1.5319329, -1.5423635, -1.5527354, -1.5630490, -1.5733047,
     -1.5835030, -1.5936443, -1.6037289, -1.6137574, -1.6237302,
     -1.6336476, -1.6435100, -1.6533179, -1.6630717, -1.6727717,
     -1.6824184, -1.6920122, -1.7015533, -1.7110423, -1.7204795,
     -1.7298653, -1.7392001, -1.7484841, -1.7577179, -1.7669017,
     -1.7760360, -1.7851210, -1.7941572, -1.8031449, -1.8120845,
     -1.8209763, -1.8298206, -1.8386178, -1.8473682, -1.8560722,
     -1.8647301, -1.8733423, -1.8819090, -1.8904306, -1.8989075,
     -1.9073399, -1.9157281, -1.9240725, -1.9323734, -1.9406312,
     -1.9488460, -1.9570182, -1.9651482, -1.9732362, -1.9812825,
     -1.9892875, -1.9972514, -2.0051744, -2.0130570, -2.0208994,
     -2.0287018, -2.0364646, -2.0441880, -2.0518723, -2.0595179,
     -2.0671248, -2.0746935, -2.0822243, -2.0897173, -2.0971728,
     -2.1045911, -2.1119725, -2.1193172, -2.1266255, -2.1338976,
     -2.1411338, -2.1483344, -2.1554995, -2.1626294, -2.1697245,
     -2.1767848, -2.1838107, -2.1908024, -2.1977602, -2.2046842,
     -2.2115747, -2.2184320, -2.2252562, -2.2320477, -2.2388065,
     -2.2455330, -2.2522273, -2.2588898, -2.2655206, -2.2721198,
     -2.2786879, -2.2852249, -2.2917310, -2.2982065, -2.3046517,
     -2.3110666, -2.3174515, -2.3238066, -2.3301321, -2.3364283,
     -2.3426952, -2.3489332, -2.3551423, -2.3613229, -2.3674750,
     -2.3735990, -2.3796949, -2.3857629, -2.3918033, -2.3978163,
     -2.4038019, -2.4097605, -2.4156921, -2.4215971, -2.4274754,
     -2.4333274, -2.4391532, -2.4449529, -2.4507268, -2.4564750,
     -2.4621977, -2.4678950, -2.4735672, -2.4792143, -2.4848367,
     -2.4904343, -2.4960074, -2.5015562, -2.5070807, -2.5125813,
     -2.5180579, -2.5235108, -2.5289402, -2.5343462, -2.5397288,
     -2.5450884, -2.5504251, -2.5557389, -2.5610300, -2.5662987,
     -2.5715450, -2.5767690, -2.5819710, -2.5871511, -2.5923094,
     -2.5974460, -2.6025611, -2.6076548, -2.6127274, -2.6177788,
     -2.6228092, -2.6278188, -2.6328077, -2.6377761, -2.6427240,
     -2.6476517, -2.6525591, -2.6574466, -2.6623141, -2.6671618,
     -2.6719898, -2.6767983, -2.6815874, -2.6863573, -2.6911079,
     -2.6958395, -2.7005521, -2.7052460, -2.7099212, -2.7145777,
     -2.7192159, -2.7238357, -2.7284372, -2.7330207, -2.7375861,
     -2.7421337, -2.7466635, -2.7511756, -2.7556701, -2.7601472,
     -2.7646070, -2.7690495, -2.7734750, -2.7778833, -2.7822748,
     -2.7866495, -2.7910074, -2.7953488, -2.7996736, -2.8039821,
     -2.8082742, -2.8125501, -2.8168100, -2.8210538, -2.8252817,
     -2.8294938, -2.8336902, -2.8378710, -2.8420362, -2.8461860,
     -2.8503205, -2.8544397, -2.8585438, -2.8626328, -2.8667068,
     -2.8707660, -2.8748103, -2.8788400, -2.8828550, -2.8868555,
     -2.8908416, -2.8948133, -2.8987707, -2.9027139, -2.9066430,
     -2.9105582, -2.9144593, -2.9183466, -2.9222202, -2.9260800,
     -2.9299263, -2.9337590, -2.9375782, -2.9413841, -2.9451767,
     -2.9489561, -2.9527223, -2.9564754, -2.9602156, -2.9639429,
     -2.9676573, -2.9713589, -2.9750479, -2.9787243, -2.9823881,
     -2.9860394, -2.9896783, -2.9933049, -2.9969193, -3.0005214,
     -3.0041115, -3.0076895, -3.0112555, -3.0148096, -3.0183518,
     -3.0218823, -3.0254011, -3.0289082, -3.0324038, -3.0358878,
     -3.0393604, -3.0428216, -3.0462715, -3.0497101, -3.0531375,
     -3.0565538, -3.0599591, -3.0633533, -3.0667366, -3.0701090,
     -3.0734706, -3.0768214, -3.0801616, -3.0834910, -3.0868099,
     -3.0901183, -3.0934162, -3.0967037, -3.0999808, -3.1032477,
     -3.1065043, -3.1097507, -3.1129870, -3.1162132, -3.1194294,
     -3.1226357, -3.1258320, -3.1290184, -3.1321951, -3.1353620,
     -3.1385193, -3.1416668, -3.1448048, -3.1479333, -3.1510522,
     -3.1541618, -3.1572619, -3.1603527, -3.1634342, -3.1665065,
     -3.1695696, -3.1726235, -3.1756683, -3.1787041, -3.1817310,
     -3.1847488, -3.1877578, -3.1907579, -3.1937492, -3.1967317,
     -3.1997056, -3.2026707, -3.2056272, -3.2085752, -3.2115146,
     -3.2144455, -3.2173680, -3.2202821, -3.2231878, -3.2260852,
     -3.2289743, -3.2318552, -3.2347280, -3.2375925, -3.2404490,
     -3.2432974, -3.2461378, -3.2489702, -3.2517947, -3.2546112,
     -3.2574199, -3.2602208, -3.2630139, -3.2657993, -3.2685770,
     -3.2713470, -3.2741094, -3.2768642, -3.2796115, -3.2823512,
     -3.2850835, -3.2878083, -3.2905258, -3.2932359, -3.2959386,
     -3.2986341, -3.3013224, -3.3040034, -3.3066772, -3.3093439,
     -3.3120035, -3.3146560, -3.3173015, -3.3199400, -3.3225715,
     -3.3251960, -3.3278137, -3.3304245, -3.3330285, -3.3356256,
     -3.3382160, -3.3407997, -3.3433766, -3.3459469, -3.3485106,
     -3.3510676, -3.3536181, -3.3561620, -3.3586994, -3.3612304,
     -3.3637549, -3.3662729, -3.3687846, -3.3712899, -3.3737889,
     -3.3762816, -3.3787681, -3.3812483, -3.3837223, -3.3861901,
     -3.3886517, -3.3911073, -3.3935567, -3.3960001, -3.3984374,
     -3.4008687, -3.4032941, -3.4057135, -3.4081270, -3.4105346,
     -3.4129363, -3.4153322, -3.4177222, -3.4201065, -3.4224850,
     -3.4248577, -3.4272248, -3.4295862, -3.4319419, -3.4342920,
     -3.4366365, -3.4389754, -3.4413087, -3.4436365, -3.4459589,
     -3.4482757, -3.4505871, -3.4528930, -3.4551936, -3.4574887,
     -3.4597785, -3.4620630, -3.4643421, -3.4666160, -3.4688846,
     -3.4711480, -3.4734062, -3.4756591, -3.4779069, -3.4801495,
     -3.4823871, -3.4846195, -3.4868468, -3.4890691, -3.4912863,
     -3.4934986, -3.4957058, -3.4979081, -3.5001054, -3.5022978,
     -3.5044853, -3.5066679, -3.5088456, -3.5110185, -3.5131866,
     -3.5153499, -3.5175084, -3.5196621, -3.5218112, -3.5239554,
     -3.5260950, -3.5282299, -3.5303602, -3.5324858, -3.5346068,
     -3.5367232, -3.5388350, -3.5409422, -3.5430450, -3.5451431,
     -3.5472368, -3.5493260, -3.5514108, -3.5534911, -3.5555669,
     -3.5576384, -3.5597054, -3.5617681, -3.5638264, -3.5658804,
     -3.5679301, -3.5699755, -3.5720166, -3.5740534, -3.5760859,
     -3.5781143, -3.5801384, -3.5821583, -3.5841741, -3.5861857,
     -3.5881931, -3.5901964, -3.5921956, -3.5941907, -3.5961817,
     -3.5981687, -3.6001516, -3.6021305, -3.6041053, -3.6060762,
     -3.6080431, -3.6100060, -3.6119650, -3.6139200, -3.6158711,
     -3.6178184, -3.6197617, -3.6217011, -3.6236367, -3.6255685,
     -3.6274964, -3.6294205, -3.6313408, -3.6332574, -3.6351701,
     -3.6370791, -3.6389844, -3.6408859, -3.6427838, -3.6446779,
     -3.6465684, -3.6484552, -3.6503383, -3.6522178, -3.6540937,
     -3.6559660, -3.6578347, -3.6596997, -3.6615613, -3.6634192,
     -3.6652737, -3.6671245, -3.6689719, -3.6708158, -3.6726562,
     -3.6744931, -3.6763266, -3.6781566, -3.6799831, -3.6818063,
     -3.6836260, -3.6854423, -3.6872553, -3.6890648, -3.6908710,
     -3.6926739, -3.6944734, -3.6962696, -3.6980625, -3.6998521,
     -3.7016384, -3.7034215, -3.7052012, -3.7069778, -3.7087511,
     -3.7105211, -3.7122879, -3.7140516, -3.7158120, -3.7175693,
     -3.7193234, -3.7210743, -3.7228221, -3.7245668, -3.7263083,
     -3.7280468, -3.7297821, -3.7315143, -3.7332435, -3.7349696,
     -3.7366926, -3.7384126, -3.7401295, -3.7418435, -3.7435544,
     -3.7452623, -3.7469672, -3.7486692, -3.7503681, -3.7520641,
     -3.7537572, -3.7554473, -3.7571345, -3.7588187, -3.7605001,
     -3.7621786, -3.7638541, -3.7655268, -3.7671966, -3.7688636,
     -3.7705277, -3.7721890, -3.7738474, -3.7755031, -3.7771559,
     -3.7788059, -3.7804531, -3.7820976, -3.7837392, -3.7853781,
     -3.7870143, -3.7886477, -3.7902784, -3.7919063, -3.7935315,
     -3.7951541, -3.7967739, -3.7983910, -3.8000055, -3.8016173,
     -3.8032264, -3.8048329, -3.8064367, -3.8080379, -3.8096365,
     -3.8112324, -3.8128258, -3.8144165, -3.8160046, -3.8175902,
     -3.8191732, -3.8207536, -3.8223315, -3.8239068, -3.8254796,
     -3.8270498, -3.8286175, -3.8301827, -3.8317454, -3.8333056,
     -3.8348633, -3.8364185, -3.8379712, -3.8395215, -3.8410693,
     -3.8426147, -3.8441576, -3.8456981, -3.8472361, -3.8487718,
     -3.8503050, -3.8518358, -3.8533642, -3.8548902, -3.8564139,
     -3.8579351, -3.8594540, -3.8609705, -3.8624847, -3.8639966,
     -3.8655061, -3.8670132, -3.8685181, -3.8700206, -3.8715208,
     -3.8730188, -3.8745144, -3.8760077, -3.8774988, -3.8789876,
     -3.8804741, -3.8819584, -3.8834404, -3.8849201, -3.8863977,
     -3.8878730, -3.8893460, -3.8908169, -3.8922855, -3.8937520,
     -3.8952162, -3.8966782, -3.8981381, -3.8995958, -3.9010513,
     -3.9025047, -3.9039559, -3.9054049, -3.9068518, -3.9082966,
     -3.9097392, -3.9111797, -3.9126181, -3.9140544, -3.9154886,
     -3.9169206, -3.9183506, -3.9197785, -3.9212043, -3.9226280,
     -3.9240497, -3.9254693, -3.9268868, -3.9283023, -3.9297158,
     -3.9311272, -3.9325365, -3.9339439, -3.9353492, -3.9367525,
     -3.9381538, -3.9395531, -3.9409504, -3.9423457, -3.9437391,
     -3.9451304, -3.9465198, -3.9479072, -3.9492926, -3.9506761,
     -3.9520576, -3.9534372, -3.9548149, -3.9561906, -3.9575644,
     -3.9589362, -3.9603061, -3.9616742, -3.9630403, -3.9644045,
     -3.9657668, -3.9671272, -3.9684858, -3.9698424, -3.9711972,
     -3.9725501, -3.9739012, -3.9752504, -3.9765977, -3.9779432,
     -3.9792869, -3.9806287, -3.9819686, -3.9833068, -3.9846431,
     -3.9859776, -3.9873103, -3.9886411, -3.9899702, -3.9912975,
     -3.9926230, -3.9939467, -3.9952686, -3.9965887, -3.9979071,
     -3.9992237, -4.0005385, -4.0018516, -4.0031629, -4.0044724,
     -4.0057802, -4.0070863, -4.0083907, -4.0096933, -4.0109941,
     -4.0122933, -4.0135907, -4.0148865, -4.0161805, -4.0174728,
     -4.0187634, -4.0200524, -4.0213396, -4.0226252, -4.0239090,
     -4.0251912, -4.0264718, -4.0277506, -4.0290278, -4.0303034,
     -4.0315772, -4.0328495, -4.0341201, -4.0353890, -4.0366563,
     -4.0379220, -4.0391860, -4.0404485, -4.0417093, -4.0429685,
     -4.0442261, -4.0454820, -4.0467364, -4.0479892, -4.0492404,
     -4.0504899, -4.0517380, -4.0529844, -4.0542292, -4.0554725,
     -4.0567142, -4.0579543, -4.0591929, -4.0604299, -4.0616654,
     -4.0628993, -4.0641316, -4.0653625, -4.0665917, -4.0678195,
     -4.0690457, -4.0702704, -4.0714936, -4.0727152, -4.0739354,
     -4.0751540, -4.0763711, -4.0775867, -4.0788009, -4.0800135,
     -4.0812246, -4.0824343, -4.0836424, -4.0848491, -4.0860543,
     -4.0872580, -4.0884603, -4.0896611, -4.0908604, -4.0920583,
     -4.0932547, -4.0944496, -4.0956432, -4.0968352, -4.0980259,
     -4.0992150, -4.1004028, -4.1015891, -4.1027740, -4.1039575,
     -4.1051396, -4.1063202, -4.1074994, -4.1086772, -4.1098537,
     -4.1110287, -4.1122023, -4.1133745, -4.1145453, -4.1157147,
     -4.1168828, -4.1180495, -4.1192147, -4.1203786, -4.1215412,
     -4.1227023, -4.1238622, -4.1250206, -4.1261777, -4.1273334,
     -4.1284878, -4.1296408, -4.1307925, -4.1319428, -4.1330918,
     -4.1342394, -4.1353857, -4.1365307, -4.1376744, -4.1388167,
     -4.1399577, -4.1410974, -4.1422358, -4.1433729, -4.1445087,
     -4.1456431, -4.1467763, -4.1479081, -4.1490387, -4.1501679,
     -4.1512959, -4.1524226, -4.1535480, -4.1546721, -4.1557949,
     -4.1569165, -4.1580368, -4.1591558, -4.1602736, -4.1613901,
     -4.1625053, -4.1636192, -4.1647320, -4.1658434, -4.1669536,
     -4.1680626, -4.1691703, -4.1702768, -4.1713820, -4.1724860,
     -4.1735888, -4.1746904, -4.1757907, -4.1768898, -4.1779876,
     -4.1790843, -4.1801797, -4.1812739, -4.1823669, -4.1834587,
     -4.1845493, -4.1856387, -4.1867269, -4.1878139, -4.1888997,
     -4.1899843, -4.1910678, -4.1921500, -4.1932311, -4.1943109,
     -4.1953896, -4.1964671, -4.1975435, -4.1986186, -4.1996927,
     -4.2007655, -4.2018372, -4.2029077, -4.2039770, -4.2050452,
     -4.2061123, -4.2071782, -4.2082429, -4.2093065, -4.2103690, -4.2114303],

    # G3 is G evaluated at z = -100:0.1:0;
    [0, -0.19350737, -0.37469671, -0.54450717, -0.70380123, -0.85337121,
     -0.99394515, -1.1261923, -1.2507279, -1.3681180, -1.4788833,
     -1.5835030, -1.6824184, -1.7760360, -1.8647301, -1.9488460,
     -2.0287018, -2.1045911, -2.1767848, -2.2455330, -2.3110666,
     -2.3735990, -2.4333274, -2.4904343, -2.5450884, -2.5974460,
     -2.6476517, -2.6958395, -2.7421337, -2.7866495, -2.8294938,
     -2.8707660, -2.9105582, -2.9489561, -2.9860394, -3.0218823,
     -3.0565538, -3.0901183, -3.1226357, -3.1541618, -3.1847488,
     -3.2144455, -3.2432974, -3.2713470, -3.2986341, -3.3251960,
     -3.3510676, -3.3762816, -3.4008687, -3.4248577, -3.4482757,
     -3.4711480, -3.4934986, -3.5153499, -3.5367232, -3.5576384,
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